TLE and position/velocity errors
The page Calculations for the Earth's artificial satellites shows the errors for the IRNSS-1H satellite when the TLE elements are used directly, without SGP4/SDP4 "decoding". Here the errors are shown for 464 satellites.
Let \(\vec{R}_{true}\) and \(\vec{V}_{true}\) be the satellite position and velocity correctly calculated for the TLE epoch by means of the SGP4.
Let \(\vec{R}_{wrong}\) and \(\vec{V}_{wrong}\) be the satellite position and velocity wrongly calculated for the TLE epoch considering the TLE elements as if they were osculating elements. One might think to use those elements to calculate the position and velocity of the satellite using the algorithm explained, for example, in this (small) PDF paper: Keplerian Orbit Elements -> Cartesian State Vectors.
The following table shows the error: \(err=\sqrt{(x_{true} - x_{wrong})^2 + (y_{true} - y_{wrong})^2 + (z_{true} - z_{wrong})^2}\), where x, y and z represent the position/velocity components.
For each satellite, the table shows:
Satellite: satellite name;
ID: satellite NORAD ID;
Orbit: average perigee and apogee altitude over a reference sphere with radius of 6371 km;
Rave: average position error [km];
Rmax: maximum position error [km];
Vave: average velocity error [m/s];
Vmax: maximum velocity error [m/s].
For example, if we consider Aeolus, its position calculated with the wrong procedure will be on average 12.5 km away from the "true" position (calculated with SGP4); while the velocity will differ on average by 5.5 m/s.
The number of the TLEs used for the calculations varies from 51 (STARLINK-1084) to 18472 (ISS), the average is 1265 TLEs/satellite, the total number of the used TLEs is 587062.